LIOUVILLE TYPE THEOREMS OF SEMILINEAR EQUATIONS WITH SQUARE SUM OF VECTOR FIELDS

• 来源期刊: 偏微分方程（英文版）
• 学科: 数学
• 关键词: Liouville type theorem superlinear equation local Hormander con-dition square sum operator generalized cone domain.
• 年，卷（期）: 2005,（2）
• 页码范围: 149-153
• 页数: 5页
• 分类号: O175.3.
• 语种: 英文

摘要

Let Xj, j = 1,…, k, be first order smooth quasi-homogeneous vector fields on Rn with the property that the dimension of the Lie algebra generated by these vector fields is n at x = 0 and X*j = -Xj, j = 1,………, k. Let L = ∑ik=l Xi2. In this paper, we study the nonnegative solutions of semilinear equation Lu +f(x, u) = 0 (or ≤ 0 ) in Rn and generalized cone domain, respectively, and prove that the solutions must be vanish under some suitable conditions.